Electro-thermal performance evaluation of a prismatic battery pack for an electric vehicle

: In recent years, electric vehicles (EVs) have grown in popularity as a viable way to reduce greenhouse gas emissions by replacing conventional vehicles. The need for EV batteries is steadily increasing. An essential and expensive part of electric transportation is the battery. The operating temperature of the lithium-ion (Li-ion) battery signi ﬁ cantly impacts the performance of the EV battery pack. Battery packs undergo temperature ﬂ uctuations during the charging and discharging procedures due to internal heat generation, necessitating an examination of the temperature distribution of the battery pack. The geometrical spacing between cells is considered larger and identical and is kept open on two sides for free air circulation. A novel battery thermal management system (BTMS) design is required to e ﬀ ectively dissipate heat from the prismatic battery pack module. The electro-thermal behaviour of the prismatic Li-ion battery pack module was investigated based on the high charge/discharge rate. This study presents the development of a three-dimensional free open-source OpenFOAM computational ﬂ uid dynamics model for prismatic cell battery packs that simulates heat generation, air ﬂ ow ﬁ eld, and temperature distribution across the width and depth of the battery pack module. The prismatic battery pack simulation results are compared with the experimental and simulation results of the cylindrical battery pack. It was also revealed that prismatic cells generate more heat on the backside, requiring battery packs to have increased cooling and space between individual cells to ensure su ﬃ cient air circulation for cooling and gas removal. The BTMS is improved by designing with increased space among the prismatic battery cells as compared with the conventional prismatic cell battery pack design.


Introduction
In the present era, the existence of global warming and environmental degradation poses a significant threat to the well-being and overall health of individuals.In recent times, there has been a growing trend towards the adoption of vehicle electrification.This approach is widely recognized as a highly promising strategy for mitigating greenhouse gas emissions.By removing tailpipe CO 2 emissions from traditional petrol or diesel internal combustion engine vehicles, electrification offers a significant potential for reducing environmental impact [1,2].The virtues of electric vehicles (EVs) have been widely acknowledged as a viable alternative to conventional automobiles in mitigating environmental pollution.According to projections, the global demand for electric car batteries is anticipated to exceed 1,300 GW h by the year 2030, representing a tenfold increase compared to the levels observed in 2020 [3][4][5].The world has been paying more attention to electric and hybrid electric vehicles (HEVs) because of the belief that they can help to solve problems like energy shortages and pollution [5][6][7].Currently, Li-ion batteries provide a notable advantage over other commercially available batteries due to their better characteristics, including power density, high energy, low self-discharge rate, and minimal memory effect.The lithium battery pack holds significant importance in both EVs and HEVs, as it serves as a crucial component responsible for powering the vehicles and influencing their overall performance.
Several factors affect the amount of heat created by the battery of EVs [8,9].These factors include the C-rate, charge/ discharge current, and the state of charge (SOC), which is closely linked to electrochemical reactions and the diffusion of lithium ions.Elevated temperatures enhance electrochemical processes and reduce internal resistance.Electrochemistry is the quantity of heat produced that is greatly affected by active materials.As the battery ages, the health status of the battery decreases, and the body's internal resistance tends to increase.The effectiveness of the Li-ion battery pack depends on the temperature of each individual cell.The optimal operational temperature range for the lithium battery cell is typically seen to be within the range of 20-40 °C [10][11][12][13][14][15][16].Therefore, it is imperative to implement a battery thermal management system (BTMS) to effectively disperse the heat produced by the battery cells and ensure the appropriate temperature of the cells during the operation of the Li-ion battery pack.Numerous thermal management techniques have been devised to facilitate the dissipation of heat from the battery pack using commercial software's [17][18][19][20].Among the several cooling technologies available, air cooling is frequently employed due to its affordability and straightforward design.Figure 1 illustrates the various cooling systems that can be employed for the purpose of cooling Li-ion batteries.
Air cooling systems utilize air as the primary medium for thermal transfer.The intake air can be sourced either directly from the atmosphere or from the cabin or mechanically induced by a fan.Active systems have the capability to provide extra cooling or heating capacity.Active systems are limited to a maximum power of 1 kW, whereas passive systems can provide cooling or heating power in the range of hundreds of watts [21][22][23][24][25][26][27].The liquid cooling system uses water as the coolant to lower the temperature of the battery.The liquid cooling system is widely utilized due to its practical design and excellent cooling efficiency.Dielectric liquid cooling, sometimes referred to as direct-contact liquid cooling, utilizes a cooling system that is capable of making direct contact with the battery cells.The alternative method involves using a conducting liquid, also known as indirect-contact liquid, which can only come into contact with the battery cells indirectly [28][29][30][31][32].This can be achieved by using a mixture of ethylene glycol and water.The designs for various layouts are contingent upon the specific type of the liquid employed.The conventional arrangement for direct-contact liquid involves immersing modules in mineral oil.Indirect-contact liquid cooling options for the battery module include a jacket surrounding the module, individual tubing around each module, positioning the modules on a cooling/heating plate, or integrating the module with cooling/heating fins and plates [15,16,21,22,33,34].Both of these groups favour the use of indirect contact solutions to enhance the isolation between the battery module and its surroundings, hence leading to enhanced safety performance.
Researchers have always focused on developing the physical design of the cooling plate and its channels in the liquid cooling system.They fabricate different designs by targeting parameters such as coolant pressure drop across the channels of the cooling plates and cell core temperature.Phase-change material (PCM) is a substance that absorbs heat during the melting process and stores it as latent heat until it reaches its maximum value [35][36][37][38][39][40][41][42][43][44].During a certain period, the temperature is maintained at the melting point, and then the temperature increase is postponed.In the BTMS, PCM functions as a conductor and buffer.Furthermore, another BTMS system, such as a liquid cooling or air cooling system, is always combined with the PCM to manage the battery core temperature.Among all the BTMS, it is considered the most active BTMS for building the simulation platform.Figure 2 shows the OpenFOAM computational fluid dynamics (CFD) analysis flow chart for the process of creating the simulation environment.
The spacing distribution among the battery cells is a critical factor among the several structural characteristics that impact the cooling efficiency of the system.The cell spacing distribution utilized in the prismatic battery module was adopted, as depicted in Figure 3(a) and (b).The airflow direction and dimensions of the battery pack are shown in Figure 3.The implementation of these spacings has resulted in an enhancement of thermal performance of the BTMS.
The findings indicate that it is possible to regulate the maximum temperature differential of the battery pack to a range of 3°C.This study investigated the impact of longitudinal and transverse spacings on the cooling performance of the battery pack with aligned and staggered arrays.Prior research has demonstrated that the cooling efficiency of the BTMS can be significantly enhanced by manipulating the Electro-thermal performance evaluation of a prismatic battery pack  3 distribution of cell spacing.The study was an examination of the increased spacing in a prismatic battery pack, specifically in relation to the dimensions of a cylindrical battery pack.The focus was on comparing the flow fields and temperature distributions within the prismatic battery pack.The temperature distribution within the prismatic battery pack has been observed to be within acceptable limits and has shown improvement.
This work simulated the creation of heat and the distribution of temperature across the prismatic battery pack module using the open-source, free OpenFOAM CFD software.The battery flow field and the thermal runaway behaviour of prismatic battery pack modules are also examined in detail.Results from OpenFOAM on prismatic battery packs were checked against experimental and Ansys data on cylindrical battery packs found in the accessible literature [12,13,[45][46][47].
The subsequent sections of this article are structured in the following manner: Section 2 presents the material and methods; Section 3 deals with thermal modelling; Section 4 discusses the numerical results and discussions in detail; and Section 5 presents the conclusions.

Materials and methods
In this study, the prismatic cell battery pack, the transient thermal behaviour of stacked Li-ion battery modules when cooled by forced air, and the heat transfer between the individual cells were all taken into account.The OpenFOAM CFD software was used to simulate a battery module.It was made up of nine prismatic Li-ion cells whose sizes were taken from the literature to compare [12][13][14].The distance between each cell's neighbours, both horizontally (L) and vertically (W), is 3 R, and the width and depth of the battery module are always 10 R. In the X-plan, consider the direction of air flow from left to right.
Table 1 lists the thermophysical and chemistry properties of the Li-ion cell that were used to make the case file for the simulation.The material in the battery pack is considered to be isotropic, and the cells are treated as a single unit with constant thermal conductivity and specific heat [14][15][16][17].Figure 4 shows that the battery module was modelled in OpenFOAM CFD using different mesh sizes, including coarse and fine meshes of prismatic batteries.Fine shapes are taken into account to make simulations more accurate and less errors.
The heat generation of the batteries, the total heat can be given by equation ( 1), the total heat generation Q gen in battery cell can be divided into three parts reaction heat (Q r ), polarization heat (Q p ), and joule heat (Q j ): The battery's heat generation from joule heating is often referred to as a gradient potential, and the cell's source resistance is associated with electrochemical reactions.It is important to note that joule heating is consistently regarded as a positive value [16,23,24].The heat generated during the charging and discharging operation is attributable to the entropy.The occurrence of endothermic or exothermic events might result in either a positive value or a negative value.The heat generation rate of the lithium-ion battery utilized in the simulation.The quantification of heat generated through reaction heating can be achieved by employing equation ( 2) as follows: In the context of representing the current during the charging or discharging process, it is important to consider the cell voltage (E) and the open circuit voltage (E oc ).The dependence of the source resistance (R) on the battery temperature (T b ) has been observed in previous studies [9,17].This relationship can be mathematically represented by equation ( 3 (3) Resistance is expressed in milli ohms, while cell temperature is measured in degrees Celsius.The calculation of joule heat generation is determined using equation (4).
The polarization heating is determined using equation (5): where R t is the total resistance, R e is the pure resistance, T b is the cell's temperature.Based on equations ( 1)-( 5), an OpenFOAM-coded function object for a user-defined function (UDF) is written for the creation of heat in a prismatic battery pack cell.

Numerical modelling
The mechanism of heat generation is examined in lithium batteries, and the model of heat generation is summarized.
The lithium battery's operating temperature has a significant effect on EV's efficacy.The rate at which heat is produced within a battery during charging and discharging has an effect on its temperature.SOC, ambient temperature, and operating current influence the quantity of joule heat and reaction heat produced [12,14].The numerical approach and validation process utilize a simplified model of battery heat generation and meshing has been done and shown in Figure 4. Constant values for thermal conductivity and other physical properties can be employed in this case, as the selected battery material exhibits isotropy.The utilization of this equation is predicated on the assumption that the temperature within the cell remains constant.Hence, the utilization of a lumped capacitance model is necessary to ensure precise application of the equation.The Biot  Electro-thermal performance evaluation of a prismatic battery pack  5 number (Bi) is employed in the realm of heat transfer theory to assess the validity of this assumption.The aforementioned quantity is a dimensionless parameter that quantifies the relationship between internal and exterior heat transfer in comparison to internal conduction, as represented in equation ( 6) [18]: where h represents the convective heat transfer related to the cooling medium (air), k b represents the thermal conductivity of the battery material, and L c represents the characteristics length that was derived by equation (7).
where V b and A s represent the volume and area, respectively, of an individual battery cell.The upper and lower surfaces of the battery cell are not taken into account when determining the overall surface area.Based on the available evidence, it can be inferred that the predominant route of heat transmission in this context is radial heat transfer from the battery cells, as indicated by previous studies [19][20][21].The heat transfer coefficient in this arrangement is limited to a maximum value of 25 W•m −2 •K −1 , as determined by the air flow velocity employed.To utilize the lumped capacitance model, it is necessary for the estimated Biot number to be less than 0.1.Equations ( 1)-( 5) elucidate the volumetric characteristic of the heat-generating source term.Finite volume approaches are commonly utilized in numerical investigations.The OpenFOAM CFD software is employed for the purpose of generating and meshing a three-dimensional representation of a prismatic battery module.The software exhibits a multitude of applications, enabling the resolution of a diverse range of issues.These encompass intricate fluid dynamics scenarios including chemical processes, turbulence, and heat transport, alongside challenges in acoustics, solid mechanics, and electromagnetics.The increase in the interior temperature of the battery is a consequence of the governing equations that are required to uphold energy balance.Consequently, the temperature of the battery can be controlled by modulating the pace at which thermal energy is dissipated into the surrounding environment.The rate at which the temperature of the battery increases will be reduced if a greater amount of heat is dissipated.Hence, it is imperative to accurately formulate the energy balance equation, encompassing heat generation and heat transport, while considering suitable boundary conditions, to predict the temperature of a battery.Equation ( 8) represents the energy balance equation that characterizes the thermal distribution within the battery.During the process of battery discharge, the computational domain is analysed by solving three-dimensional governing equations that account for the conservation of mass, momentum, and energy.The governing equation for the scenario involving a solid domain is written as follows [9,16]: where heat production (Q gen ) is indicated in equation ( 1).ρ b , C p,b , and k f are used to represent the density, specific heat, and thermal conductivity of battery material, respectively.The simulation of conjugate heat transfer involves the connection of the fluid domain, which represents the airflow, with the solid domain, which represents heat conduction accompanied with internal volumetric heat creation.
A prevalent approach for representing the heat exchanger in the BTMS involves employing a convective boundary condition at the surface of the battery.The temperature of the battery is influenced by several factors, including the heat generated internally, the thermal properties of the battery, the convective heat transfer coefficient of the heat exchanger, and the ambient temperature.This relationship is described by the governing equation and the boundary condition.Figure 3b illustrates the boundary conditions applied to the prismatic battery module, which consists of a continuous and uniform flow of cooling air at the module's inlet.The battery module is equipped with ventilation openings on both sides to facilitate the unrestricted circulation of cooling air.The velocity intake is assigned to the left side of the battery domain, while the exit is treated as a pressure outlet.To regulate temperature, ambient air is set at a temperature of 22°C.In the CFD model of the battery pack, the air was represented as a fluid zone, while the battery was represented as a solid zone.The term "coupled wall condition" pertains to the battery surfaces that separate the air zone.The slip boundary requirement does not apply to the limits of the battery.The experimental and commercial software results were validated by employing a sensitivity analysis of the mesh in the numerical free open-source OpenFOAM CFD model.

Results and discussion
Numerical simulations using OpenFOAM CFD software were conducted to analyse the battery discharge condition at the rated current.The flow field of the battery module is determined by the heat output of each of its nine cells.The computational results, encompassing the internal flow field and temperature distribution within the battery module, are presented in the form of a transient thermal response module.Battery cells produce thermal energy, the magnitude of which can be quantified using equation (1).During the initial stage of the procedure, the battery cells are maintained at a temperature of approximately 22°C, which closely corresponds to the surrounding atmospheric temperature.Figure 5 illustrates the temperature distribution and surface temperature of the prismatic cell battery, both of which increase due to the discharge of internal heat.By utilizing the three-dimensional temperature contours depicted in Figure 5(a-f), one can observe the comprehensive temperature variations and flow patterns within the module at a specific time of t = 50 s.During this time interval, the heat generation by the cell is relatively low.Subsequently, between t = 100 and 300 s, the heat generation gradually increases.Finally, at t = 400-500 s, the heat generation reaches a high level, as evidenced by the colour range of the cells and the surrounding areas, where the temperature is notably elevated.The temperature distribution in the cells of the first row is marginally lower compared to the cells in the subsequent two rows due to their direct exposure to the input of cool air.The battery module utilizes cooling air at an equivalent temperature to ensure optimal operational efficiency.The thermal output of the module has the potential to impact the efficiency of the battery.The process of circulating cooling air at a reduced supply temperature effectively eliminates excess heat from the battery module.
The thermal behaviour of the battery is primarily influenced by the battery cell design, the spacing between neighbouring cells, and the presence and temperature of cooling fluids.Figure 6 illustrates the utilization of threedimensional temperature contours to represent the complete range of temperature distributions and flow patterns within the module.The module exhibits evident hotspots and temperature fluctuations.The presence of isolated hotspots undermines the dependability of the battery.Four planes were selected at different heights (h = 25, 50, 75, and 90 mm) to investigate localized heat spots.The evaluation was conducted at a discharge time of 500 s, with supply air conditions of 22°C and a velocity of 0.1 m•s −1 , as depicted in Figure 6(a-d).It is evident that the air temperature remains constant until it reaches the initial row of battery cells.Furthermore, it has been shown that the areas in close proximity to module's two lateral walls remain unaffected by the dissipation of heat generated by the cells.The local heat spot zones are identified where the air temperature is maximum in the battery pack.Figure 6 displays the temperature contours of the cooling media (air) within the prismatic battery module.Within the module, there exist localized hotspots situated behind and near to the cells.
The acquisition of such data can be facilitated through the implementation of a quantitative evaluation of ambient air temperature within the battery module.Significant variations in temperature exist between the regions, and second and third rows of cells are high.The variation in temperature gradient is evident as the depth of the module increases, with the most pronounced gradient observed towards the base surface of the module.The analysis of modulator air temperature variations provides insights into the passage of heat from the battery surface to the cooling media.The investigation also encompassed the examination of temperature regimes formed across the breadth of the module in the transverse direction.Figure 7 shows the highest temperature-heated cell among all the cells in the battery pack.The architecture of the BTMS significantly depends on the external flow that passes over the battery cell.Through the process of convection, cells have the capacity to dissipate surplus heat into their surrounding environment.Figure 8 illustrates the airflow pattern within the prismatic battery module, revealing that the air temperature reaches its peak between the rows and in proximity to the curvature of the cells.The no-slip condition boundary condition postulates that the velocity of air at the surface of the battery is zero.The airflow surrounding the battery cell undergoes a division at the moment of separation.The resultant boundary layer fully encompasses the cell.When the velocity of air decreases to zero at the stagnation point, there is a corresponding increase in pressure in that region.An increase in air velocity leads to a corresponding reduction in pressure in the direction of airflow.It is evident that the air velocities exhibit their largest magnitudes precisely at the locations of cellular gaps.A separation zone is generated in the wake of the battery cell as airflow passes over it, causing the detachment of air from the cell's surface, namely, the boundary layer that envelops the cell.
The investigation revealed that the occurrence of air recirculation and backflows within the isolation zones exhibited variations corresponding to the depth of the module.The analysis of airflow patterns within a battery module is conducted under controlled conditions of 22°C temperature and a supply air velocity of 0.1 m•s −1 .The duration of discharge is 500 s.The temperature of the cells located closer to the outlet ends is somewhat higher compared to their respective preceding cells.
The cells in row 1, namely, those indexed as 1, 2, and 3, exhibit a high level of efficiency in dissipating heat to the surrounding colder air.Cells located in row 2, specifically those with indices 4, 5, and 6 and row 3 with indices 7, 8, and 9 have the capacity to collect heat in the direction of their movement and subsequently emit it to the surrounding warmer air.By utilizing the volume-weighted Electro-thermal performance evaluation of a prismatic battery pack  7     The thermal model, incorporating an OpenFOAM UDF, is employed to compute the thermal energy generated by the battery.The present study aims to validate the computational results obtained using Open FOAM CFD and comparing with Ansys conventional design of the prismatic battery pack.Empirical evidence has demonstrated that the thermal profiles of prismatic battery packs exhibit variations contingent upon the direction of airflow, as well as the specific location within the pack's breadth and depth.As the temperature decreases, the proximity of a module to a cooling air source increases.The cells in second and third rows of the module exhibit higher temperatures compared to the first-row cells.The air temperature exhibits spatial variability in the direction of flow as well as across the breadth and depth of the module.Observations of transverse temperature gradients are made in the atmosphere.The presence of localized areas of increased heat, known as heat spots, has been verified when temperatures transition from the prescribed cooling state of 22°C to a local peak temperature of 30.94°C at a time of 500 s (t = 500 s).The highest local temperatures are primarily located at the geometric centre and last row of the module.The battery module exhibits typical flow characteristics.The battery exhibits flow separation to variable degrees across its different layers.The temperatures of battery cells undergo variations as they transition from one position inside the battery module to another.
Q j Joule heating, (Joules per second) Q p Polarization heating (Joules per second) Q r Reaction heating (Joules per second) E Cell potential (Volt) E oOpen circuit potential (Volt) RThe internal resistance of battery cell (Ω)I Current (Amp) h Convective heat transfer coefficient (W•m −2 •K −1 ) L c Characteristics length (m) Bi Biot number (-) T cell Instantaneous cell temperature (°C) K b Thermal conductivity (W•m −1 •K −1 ) C Discharge rate C p,b Specific heat (J•kg −1 K −1 ) L Length (mm) ρ b Density (kg•m −3 ) D Diameter (mm) t Time (seconds) W Vertical length (mm) L Horizontal length (mm) A s Area of a single battery cell (m 2 ) Q gen Heat generation in a cell (J•s −1 ) V bVolume of a single battery cell (m 3 ) m Mass of cell (kg)

Figure 1 :
Figure 1: Types of battery thermal management systems.

Figure 3 :
Figure 3: Prismatic battery pack module: (a) air flow direction consideration in battery pack and (b) dimensions of battery pack.

Figure 4 :
Figure 4: Meshing of the battery pack module.(a) Coarse mesh and (b) thin mesh.
Figure 9 illustrates the cell temperature of experimental results of a cylindrical module, OpenFOAM CFD, and prismatic cell temperature variations.

Figure 8 :
Figure 8: Air flow field of battery module.